4/23/2010

Olga Plamenevskaya
SUNY Stony Brook

Monodromy factorizations and symplectic fillings

By a fundamental result of Giroux, contact structures on 3-manifolds may be described via their open books decomposition. A contact manifold can arise as a boundary of a Stein domain if and only if it has a compatible open book whose monodromy is a product of positive Dehn twists. In principle, one has to examine {\em all} compatible open books to detect Stein fillings. However, a theorem of Wendl says that if a compatible open book has planar pages, all Stein fillings are compatible with the {\em given} open books. To apply this theorem, we develop combinatorial techniques to study positive monodromy factorizations in the planar case. As a result, we can classify symplectic fillings for all contact structures on L(p,1), and detect non-fillability of certain contact structures on Seifert fibered spaces. (Joint with Jeremy Van Horn-Morris.)